Local intersection cohomology of varieties of complexes

TL;DR

This paper computes the local intersection cohomology of varieties of complexes using Lusztig's geometric approach and canonical bases, providing new insights into their geometric and algebraic structure.

Contribution

It introduces a novel method combining Lusztig's geometric approach with explicit canonical basis constructions to analyze intersection cohomology of complex varieties.

Findings

Computed local intersection cohomology for varieties of complexes.

Linked geometric properties with Lusztig's canonical bases.

Enhanced understanding of the structure of irreducible components.

Abstract

We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.